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Fourier Neural Operators Learn Lyapunov Functions for Nonlinear Systems

By PulseAugur Editorial · [2 sources] ·

Researchers have developed a method to approximate Lyapunov functions for nonlinear dynamical systems using Fourier Neural Operators (FNOs). This approach aims to overcome the challenge of finding Lyapunov functions, which are crucial for stability analysis but are typically system-specific. The study establishes theoretical foundations for the Lyapunov solution operator, demonstrating its well-defined nature and continuity under certain stability assumptions. Numerical experiments show that a single trained FNO can accurately approximate Lyapunov functions across parameterized families of dynamics, highlighting the potential of neural operators in this field. AI

IMPACT Introduces a novel application of neural operators for stability analysis in nonlinear systems, potentially advancing theoretical and practical applications in control theory and robotics.

RANK_REASON Academic paper detailing a new method for approximating Lyapunov functions using neural operators. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Fourier Neural Operators Learn Lyapunov Functions for Nonlinear Systems

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Academic paper detailing a new method for approximating Lyapunov functions using neural operators. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Max Beier, Nicolas Hoischen, Sandra Hirche, Petar Bevanda ·

    Demystifying Linear Operator Learning for Control Systems

    arXiv:2609.19428v1 Announce Type: cross Abstract: This paper proposes a structured approach to learning linear operators for control systems from data. We address both structural and learning-theoretic aspects of the problem. To derive structural assumptions, we propose using the…

  2. arXiv cs.LG TIER_1 English(EN) · Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fern\'andez, Jun Liu ·

    Learning Lyapunov Operators for Nonlinear Systems

    arXiv:2609.18894v1 Announce Type: cross Abstract: Constructing Lyapunov functions for nonlinear dynamical systems is a central problem in stability analysis, yet remains challenging. Lyapunov functions are commonly characterized as solutions to first-order partial differential eq…

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